A typical problem involving the area and perimeter of a rectangle gives us the area, perimeter and/or length and width of the rectangle. We may also be given a relationship between the area and perimeter or between the length and width of the rectangle. We need to calculate some of these quantities given information about the others.

There is no solution. The solution involves the square root of negative 1.

length = 6 and width = 8/3 and the perimeter is 52/3

What is your answer?

A rectangle is shown in the diagram below. If the area is 105, what are the rectangle's dimensions and what is its perimeter?

length = 4 and width = 1.5 and the perimeter is 11

length = 15 and width = 7 and the perimeter is 44

There is no solution. The solution involves the square root of negative 1.

What is your answer?

A rectangle has a diagonal which is 3 times the width. If the area is what are the width and perimeter of this rectangle?

width = 2 and the perimeter is

width = and the perimeter is

width = and the perimeter is

What is your answer?

This type of problem involves relationships between the length and width and/or connections between the length, width, and diagonal of a rectangle. With information about the area or perimeter, we can set up equations that allow us to find the rectangle's length and width. Once these are known, we can use the formulas for area and perimeter.

Sometimes there is a need to use the Pythagorean Theorem to relate the length, width, and diagonal. It is important to take note of the fact that the diagonal is always the hypotenuse of this right triangle.